Michael is 8 years older than Omar. For the last four years, Michael and Omar have been going to the same school. Two years ago, Michael was 5 times older than Omar. How old is Michael now?
Explanation: We can use the given information to write down two equations that describe the ages of Michael and Omar. Let Michael's current age be $m$ and Omar's current age be $o$ The information in the first sentence can be expressed in the following equation: $m = o + 8$ Two years ago, Michael was $m - 2$ years old, and Omar was $o - 2$ years old. The information in the second sentence can be expressed in the following equation: $m - 2 = 5(o - 2)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $m$ , it might be easiest to solve our first equation for $o$ and substitute it into our second equation. Solving our first equation for $o$ , we get: $o = m - 8$ . Substituting this into our second equation, we get the equation: $m - 2 = 5($ $(m - 8)$ $ -$ $ 2)$ which combines the information about $m$ from both of our original equations. Simplifying the right side of this equation, we get: $m - 2 = 5m - 50$ Solving for $m$ , we get: $4 m = 48$ $m = 12$.